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Based on discrete Hartley transform algorithm, the proposed fast algorithm is implemented by the parallel Hopfield neural network which can shorten the computation length of discrete cosine transform to achieve high computation speed. The computation complexity of the proposed method is reduced comparing with the others. According to the proposed algorithm which can implement the arbitrary length of discrete cosine transform, the N-point discrete cosine transform requires 2(N-1) real multiplications and 3N-2 real additions. Thus, the algorithm has a better application prospect in signal processing.